Inoue Shōta, Eddin Sumaia Saad, Suriajaya Ade Irma
Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8602 Japan.
Institute of Financial Mathematics and Applied Number Theory, JKU Linz, Altenbergerstraße 69, 4040 Linz, Austria.
Ramanujan J. 2021;55(2):609-621. doi: 10.1007/s11139-021-00391-1. Epub 2021 Mar 20.
Let be an arithmetic function and let denote the extended Selberg class. We denote by the Dirichlet series attached to . The Laurent-Stieltjes constants of , which belongs to , are the coefficients of the Laurent expansion of at its pole . In this paper, we give an upper bound of these constants, which is a generalization of many known results.
设(f)为一个数论函数，(\mathcal{S})表示扩展塞尔伯格类。我们用(D_f(s))表示与(f)相关的狄利克雷级数。属于(\mathcal{S})的(D_f(s))的洛朗 - 斯蒂尔杰斯常数是(D_f(s))在其极点(s = 1)处的洛朗展开式的系数。在本文中，我们给出了这些常数的一个上界，它是许多已知结果的推广。
